436 Chapter 11. Machines in membranes[[Student version, January 17, 2003]]
Key formulas
- Gibbs–Donnan: If several ion species can all permeate a membrane, then in order to have
equilibrium their Nernst potentials must all agree with each other (and with the externally
imposed potential drop, if any). For example, suppose the ions are sodium, potassium, and
chloride, and letc 1 ,iandc 2 ,ibethe exterior and interior concentrations, respectively, of species
i.Then (Equation 11.5)
c 1 ,Na+
c 2 ,Na+
=
c 1 ,K+
c 2 ,K+=
c 2 ,Cl−
c 1 ,Cl−.
- Pumps: The effect of active ion pumping is to add an ATP-dependent current source to
the membrane. Making the Ohmic hypothesis givesjNa+ = gNae+(∆V−VNaNernst+ )+jpumpNa+
(Equation 11.10). HerejNa+is the flux of sodium ions,gNa+is the membrane’s conductance,
VNaNernst+ is the Nernst potential, and ∆Vis the actual potential difference across the membrane.
Further reading
Semipopular:
History: Hodgkin, 1992.
Intermediate:
Section 11.2 follows in broad outline the approach of Benedek & Villars, 2000c. See also Katz’s
classic book, Katz, 1966.
Osmoregulation: Keener & Sneyd, 1998,§2.8
Electroosmotic aspects of kidney function: Hoppensteadt & Peskin, 2002; Benedek & Villars,
2000c.
Many biochemistry and cell-biology texts describe the biochemical aspects of respiration, for
example Berg et al., 2002; Nelson & Cox, 2000; Voet & Voet, 2003; Karp, 2002.
Chemiosmotic mechanism: Atkins, 2001; Alberts et al., 1997.
Modeling of ion transport, cell volume control, and kidney function: Hoppensteadt & Peskin, 2002;
Keener & Sneyd, 1998.
Technical:
Ion Pumps: L ̈auger, 1991; Skou, 1989.
F0F1: Noji et al., 1997; Boyer, 1997; Oster & Wang, 2000.